Rendered object Blender 2.74 can't be moved
Rendering (in Cycles) is the process of taking the 3-dimentional scene and calculating the light paths (called rays) bouncing through the scene to the camera.  The end result is a 2-dimentional picture of your scene, so you can't really rotate it and look around.  Just like you can't rotate and look around a photograph you took in real life.

See my answer here for more on how Cycles works.

In order to be able to move and look around your model in perfect real time Cycles would have to perform a separate render from every possible position and angle of the camera, which is impossible.  Here a few ways to view your rendered object from multiple angles.

1. Viewport rendering

As gladys pointed out you can enable viewport rendering.  This basically re-renders the entire viewport every time you move the view.  Viewport rendering is mainly just for viewing material tweaks and the like in real time.

You can change the amount of samples used for viewport rendering in the properties panel under the render tab > sampling rollout > samples > preview.



2. Animating the object/camera

For a final output to showcase your object you may want to create an animation of either the camera moving around the object or the object itself moving.

Animation is done by setting keyframes.  A keyframe tells Blender the state you want an object to be in at a particular frame, Blender will then interpolate the object smoothly between keyframes.  To set a keyframe go to the frame you want to keyframe and hit I and choose the property you want to animate (i.e. location, rotation, scale, etc.).

Try checking out this tutorial.

3. Baking

Baking is a way of saving what the surface of a rendered object looks like to an image texture which you can then apply to the object as a shadeless shader to make the object look like it is rendered.

Unfortunately I don't have the space here to even dip into the world of texture baking but you can check out this tutorial for starters.

One thing to consider about baking is that things like gloss and transparency/refraction do not bake well as they are dependent on the viewing angle.